Study of integrable systems and tropical curves
| Project/Area Number |
26800062
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Tokai University (2017)
Aoyama Gakuin University (2014-2016) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | トロピカル幾何学 / 対称多項式 / Young盤の組み合わせ論 / 旗多様体の量子K理論 / 特異曲線 / 超離散可積分系 / 正値性 / トロピカル曲線 / 旗多様体の量子コホモロジー / 離散可積分系 / 量子コホモロジー / Totally positivity / トロピカル幾何 / Totally Positive matrix |
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| Outline of Final Research Achievements |
The tropical geometry is a kind of geometry where the usual multiplication and addition are replaced with the addition and maximum. Since it has been known that the tropical geometry admits good applications to the study of integrable system theory, the main aim of this research is to study their essential relations. The main results of this research are as follows: 1. The relation between the "quantum K-theory" of the flag variety and some special symmetric polynomials are clarified by using the algebraic method to the relativistic Toda equation. 2. The application of the tropical KP equation to various combinatoric problems of Young tableau is obtained.
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Report
(5 results)
Research Products
(12 results)
